Deterministic simulation replicating reverse shooting

I am trying to replicate the results from a simulation of a model with Tobin’s q described in the attached working paper by Herbert and Stemp.

They consider a model with capital stock, external debt, and Tobin’s q, that moves from a steady state with real interest rate r=0.03 to a new steady state with r=0.05.

They calculate the two steady states, both of course with q=1, and calculate using reverse shooting that initially, Tobin’s q must jump from 1 to 0.7872 (in a non-linear model) or to 0.5785 (linearised version) to put the model on a stable arm (Table 1 on p.14).

I tried to replicate their results using deterministic simulation in Dynare. Using Homotopy, I was able to reproduce the two steady states and use them as initval and endval conditions. The initial jump in q is, however, much smaller, to 0.9766. (I attach the mod file).

Is there something I did wrong? Is there some difference between solving for teh jump in q and what the command simul does in Dynare?

Thank you very much in advance for your help,
herbert_stemp2000_cesifo_wp266.pdf (260 KB)
herb_stemp1.mod (1.73 KB)